TRAPPING PROBLEM OF HONEYPOTS ON FRACTAL NETWORKS WITH THE STURMIAN STRUCTURE

Yuke Huang, Cheng Zeng and Yumei Xue ()
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Yuke Huang: School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, P. R. China†Key Laboratory of Mathematics and Information Network, (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing 100876, P. R. China
Cheng Zeng: ��School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264003, Shandong Province, P. R. China
Yumei Xue: �School of Mathematics and System Science, Beihang University, Beijing 100191, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 07, 1-9

Abstract: This paper studies the average trapping time of honeypots on some evolving networks. We propose a simple algorithmic framework for generating networks with Sturmian structure. From the balance property and the recurrence property of Sturmian words, we estimate the average trapping time of our proposed networks with an asymptotic expression 〈T〉t ∼ Mt(α)2t, where Mt(α) is a bounded expression related to word α ∈{0, 1}∞. We next consider networks with multi-honeypots and generalize our basic models. Additionally, we give an symmetrical method to create a series of networks with the Sturmian structure, and the average trapping time satisfies 〈T〉t ∼ 5 × 2t, which is independent of any word α. The generalized methods may have some illuminating effects on the study of networks with randomness.

Keywords: Fractal Network; Network Design; Average Trapping Time; Sturmian Words; Honeypots (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500779

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